The next generation of ground-based gravitational-wave detectors will observe coalescences of black holes and neutron stars throughout the cosmos, thousands of them with exceptional fidelity. The Science Book is the result of a 3-year effort to study the science capabilities of networks of next generation detectors. Such networks would make it possible to address unsolved problems in numerous areas of physics and astronomy, from Cosmology to Beyond the Standard Model of particle physics, and how they could provide insights into workings of strongly gravitating systems, astrophysics of compact objects and the nature of dense matter. It is inevitable that observatories of such depth and finesse will make new discoveries inaccessible to other windows of observation. In addition to laying out the rich science potential of the next generation of detectors, this report provides specific science targets in five different areas in physics and astronomy and the sensitivity requirements to accomplish those science goals. This report is the second in a six part series of reports by the GWIC 3G Subcommittee: i) Expanding the Reach of Gravitational Wave Observatories to the Edge of the Universe, ii) The Next Generation Global Gravitational Wave Observatory: The Science Book (this report), iii) 3G R&D: R&D for the Next Generation of Ground-based Gravitational Wave Detectors, iv) Gravitational Wave Data Analysis: Computing Challenges in the 3G Era, v) Future Ground-based Gravitational-wave Observatories: Synergies with Other Scientific Communities, and vi) An Exploration of Possible Governance Models for the Future Global Gravitational-Wave Observatory Network.